René Thom

René Thom was born in Montbéliard, Doubs. He was educated at the Lycée Saint-Louis and the École Normale Supérieure, both in Paris. He received his PhD in 1951 from the University of Paris. His thesis, titled Espaces fibrés en sphères et carrés de Steenrod (Sphere bundles and Steenrod squares), was written under the direction of Henri Cartan. The foundations of cobordism theory, for which he received the Fields Medal at the International Congress of Mathematicians in Edinburgh in 1958, were already present in his thesis.

After a fellowship in the United States, he went on to teach at the Universities of Grenoble (1953–1954) and Strasbourg (1954–1963), where he was appointed Professor in 1957. In 1964, he moved to the Institut des Hautes Études Scientifiques, in Bures-sur-Yvette. He was awarded the Brouwer Medal in 1970, the Grand Prix Scientifique de la Ville de Paris in 1974, and became a Member of the Académie des Sciences of Paris in 1976.

While René Thom is most known to the public for his development of catastrophe theory between 1968 and 1972, in which he uses his earlier work on differential topology to develop a general theory of biological form,[1] his academic achievements concern mostly his mathematical work on topology. In the early 1950s it concerned what are now called Thom spaces, characteristic classes, cobordism theory, and the Thom transversality theorem. Another example of this line of work is the Thom conjecture, versions of which have been investigated using gauge theory. From the mid 1950s he moved into singularity theory, of which catastrophe theory is just one aspect, and in a series of deep (and at the time obscure) papers between 1960 and 1969 developed the theory of stratified sets and stratified maps, proving a basic stratified isotopy theorem describing the local conical structure of Whitney stratified sets, now known as the Thom–Mather isotopy theorem. Much of his work on stratified sets was developed so as to understand the notion of topologically stable maps, and to eventually prove the result that the set of topologically stable mappings between two smooth manifolds is a dense set. Thom's lectures on the stability of differentiable mappings, given at the University of Bonn in 1960, were written up by Harold Levine and published in the proceedings of a year long symposium on singularities at Liverpool University during 1969-70, edited by C. T. C. Wall. The proof of the density of topologically stable mappings was completed by John Mather in 1970, based on the ideas developed by Thom in the previous ten years. A coherent detailed account was published in 1976 by Christopher Gibson, Klaus Wirthmüller, Andrew du Plessis, and Eduard Looijenga. While Thom found general recognition among the general public for the popularized version of his work on biology (later developed by Christopher Zeeman), this work struggled to gain traction among natural scientists due to the inaccessibility of its mathematics.[1]

During the last twenty years of his life Thom's published work was mainly in philosophy and epistemology, and he undertook a reevaluation of Aristotle's writings on science. In 1992, he was one of eighteen academics who sent a letter to Cambridge University protesting against plans to award Jacques Derrida an honorary doctorate.[2]

Beyond Thom's contributions to algebraic topology, he studied differentiable mappings, through the study of generic properties. In his final years, he turned his attention to an effort to apply his ideas about structural topography to the questions of thought, language, and meaning in the form of a "semiophysics".

• Thom, René (1952), "Espaces fibrés en sphères et carrés de Steenrod" (PDF), Annales Scientifiques de l'École Normale Supérieure, Série 3, 69: 109–182, doi:10.24033/asens.998, MR 0054960
• Thom, René (1954), "Quelques propriétés globales des variétés différentiables", Commentarii Mathematici Helvetici, 28: 17–86, doi:10.1007/BF02566923, MR 0061823, S2CID 120243638
• "Ensembles et morphismes stratifiés", Bulletin of the American Mathematical Society 75 (1969), 240–284.
• "Semio Physics: A Sketch", Addison Wesley, (1990), ISBN 0-201-50060-4
• Structural Stability and Morphogenesis, W. A. Benjamin, (1972), ISBN 0-201-40685-3.

• "Quelques propriétés globales des variétés differentiables"

• Petitot, Jean, ed. (1996). Logos et Théorie des Catastrophes: à partir de l'oeuvre de René Thom. Colloque de Cerisy-la-Salle 1982. Geneva: Patiño. ISBN 978-2-88213-010-5.
• Aubin, David (2004). "Forms of Explanations in the Catastrophe Theory of René Thom: Topology, Morphogenesis, and Structuralism" (PDF). In Wise, M. N. (ed.). Growing Explanations: Historical Perspective on the Sciences of Complexity. Durham: Duke University Press. pp. 95–130.
• Reilly, Brian J. (2006). "René Thom". In Kritzman, Lawrence D. (ed.). The Columbia History of Twentieth-Century French Thought. New York: Columbia University Press. pp. 663–666. ISBN 978-0-231-10791-4.
• Weil, Martin (November 17, 2002). "French Mathematician René Thom Dies". Washington Post. p. C10.
• Papadopoulos, Athanase (2018). "René Thom: Portrait Mathématique et philosophique". CNRS Editions, Paris. ISBN 978-2-271-11827-1.

Wikimedia Commons has media related to René Thom.

• O'Connor, John J.; Robertson, Edmund F., "René Thom", MacTutor History of Mathematics archive, University of St Andrews.
• René Thom at the Mathematics Genealogy Project
• Washington Post Online edition (free registration)
• Meeting René THOM